## ON IMPROVING CONNECTIVITY OF STATIC AD-HOC NETWORKS BY ADDING NODES ∗

Citations: | 5 - 0 self |

### BibTeX

@MISC{Koskinen_onimproving,

author = {Henri Koskinen and Jouni Karvo and Olli Apilo},

title = {ON IMPROVING CONNECTIVITY OF STATIC AD-HOC NETWORKS BY ADDING NODES ∗},

year = {}

}

### OpenURL

### Abstract

Ad hoc networks are by nature constructed “automatically”, by the nodes adapting to the neighboring nodes and building up a network. In this context, the network topology is random, and in particular, no connectivity is guaranteed: the nodes may be so sparsely located that they are unable to make up a

### Citations

1351 | A Survey on Sensor Networks
- Akyildiz, Su, et al.
(Show Context)
Citation Context ...ectivity, from top to bottom.sof the network. We present algorithms that suggest locations for such additional nodes. Networks where adding extraneous nodes is feasible are some sensor networks — see =-=[8]-=- for a survey on sensor networks — and such ad-hoc networks that are used in a controlled situation where some central entity can organize the deployment of the nodes. To our knowledge, the connectivi... |

632 | Voronoi diagrams - a survey of a fundamental geometric data structure
- Aurenhammer
- 1991
(Show Context)
Citation Context ...tep 1 can be completed in O(N log N) time by utilizing the Delaunay triangulation; when d = 3, the complexity of finding the minimum spanning tree has at least been brought down to O(N 4/3 log 4/3 N) =-=[1]-=-. In a higher number of dimensions, step 1 is likely to require exhaustively calculating the distance matrix of the terminal nodes, which is a quadratic task. Step 2 is linear in N if all the necessar... |

469 |
2002. Algorithms in C
- Sedgewick
(Show Context)
Citation Context ... exactly those edges that are longer than the transmission range r, in the MST calculated for all the terminal nodes. This can be seen by considering Kruskal’s algorithm for finding the MST (see e.g. =-=[4]-=-). The steps of the algorithm are thus as follows: 1 Calculate the Euclidean minimum spanning tree for N . 2 Place the relay nodes on the edges of the minimum spanning tree that are longer than r. If ... |

431 | Critical Power for Asymptotic Connectivity in Wireless Networks. Stochastic Analysis, Control, Optimization and Applications
- Gupta, Kumar
- 1998
(Show Context)
Citation Context ...his critical range is equal to the greatest edge length in the Euclidean minimum spanning tree of the nodes, as pointed out in [2]. Asymptotic scaling laws for the critical range have been derived in =-=[3]-=-. The notion of the critical range can be generalized to kconnectivity, which guarantees connectivity to prevail at the failure of any k − 1 nodes. The distributions of the critical ranges for k-conne... |

206 | Location in distributed ad-hoc wireless sensor networks
- Savarese, Rabaey, et al.
- 2001
(Show Context)
Citation Context ...ioning systems, yielding accurate enough estimates (within 10–20 m from the true position), and being cost-effective enough for implementation. Another way of positioning nodes is using triangulation =-=[9]-=-, but this requires that each part of the network has enough nodes with known positions. Thus, triangulation methods can be used to locate single nodes that are not on the coverage of other positionin... |

178 | Connectivity in ad-hoc and hybrid networks
- Dousse, Thiran, et al.
- 2002
(Show Context)
Citation Context ...etric graphs. Percolation properties of such graphs when the positions of the network nodes are distributed according to a homogeneous Poisson point process in the infinite plane have been studied in =-=[1]-=-. In the case of a finite domain, the probability of a random network being connected depends only on the probability distribution of the critical transmission range for connectivity: for a given set ... |

102 |
The complexity of computing Steiner minimal trees
- Garey, Graham, et al.
- 1977
(Show Context)
Citation Context ... to finding the Euclidean Steiner minimal tree for the set N : the optimal solution is then to place the relay nodes along the edges of this tree. Finding Steiner minimal trees is known to be NP-hard =-=[3]-=-. In the general case, our problem poses the additional complications that we are not connecting single points to each other, but clusters where the best points in the clusters for connecting to other... |

52 | Determination of critical transmission range in ad-hoc networks
- Sanchez, Manzoni, et al.
- 1999
(Show Context)
Citation Context ...critical transmission range for connectivity: for a given set of nodes, this critical range is equal to the greatest edge length in the Euclidean minimum spanning tree of the nodes, as pointed out in =-=[2]-=-. Asymptotic scaling laws for the critical range have been derived in [3]. The notion of the critical range can be generalized to kconnectivity, which guarantees connectivity to prevail at the failure... |

38 |
Movement control algorithms for realization of fault-tolerant ad hoc robot networks
- Basu, Redi
- 2004
(Show Context)
Citation Context ...ntal strategy – even if the individual steps were solved optimally – can be highly suboptimal in increasing the degree of connectivity by more than one. A somewhat related problem has been studied in =-=[14]-=-, where an ad hoc network of mobile robot nodes is already assumed to be connected, and the goal is to move the robots to make the network biconnected so that the total distance travelled by the robot... |

37 | Asymtotic critical transmission radius and critical neighbor for k-connectivity in wireless ad hoc networks
- Wan, Yi
- 2004
(Show Context)
Citation Context ...s for the purposes of simulation and empirical modelling are developed in [5], and empirical models describing the convergence of the distributions of the critical ranges to the known asymptotic ones =-=[6]-=- are presented in [7]. As an example of the findings in these studies, one may look at Figure 1 which shows the transmission range that, for nodes distributed uniformly at random in a 1 km × 1 km area... |

36 |
On the connectivity of ad hoc networks
- Bettstetter
- 2004
(Show Context)
Citation Context ...ranges for k-connectivity with any k are not known when the number of nodes is finite. Attempts to determine analytically the probability of k-connectivity of finite random networks have been made in =-=[4]-=-, based on using as an approximation the probability of every node having at least k neighbors. Efficient algorithms for determining the critical ranges for the purposes of simulation and empirical mo... |

22 |
An approach for proving lower bounds: solution of Gilbert-Pollak’s conjecture on Steiner ratio
- Du, Hwang
- 1990
(Show Context)
Citation Context ...d the underlying assumptions, and define essentially two opti∗We thank the anonymous reviewers of this paper for their constructive suggestions, and Petteri Kaski (TKK) for pointing out the reference =-=[2]-=-. † Financially supported by the Finnish Defence Forces Technical Research Centre and in part by a grant from the Nokia Foundation. ‡ Funded by the EU FP6-507572 project WIDENS. § Funded by the Academ... |

17 | Graph augmentation and related problems: theory and practice
- Hsu
- 1993
(Show Context)
Citation Context ...ph the set of edges with minimum total weight so that the resulting graph is k-connected. When k = 1, the problem reduces to finding the MST, but for any k > 1 the problem is known to be NP-hard: see =-=[13]-=- and the references therein. Thus, even with the simplest approach to making a network k-connected with k > 1, we immediately run into complex problems. In what follows, we examine the problem of maki... |

7 |
A simulation-based method for predicting connectivity in wireless multihop networks
- Koskinen
(Show Context)
Citation Context ...proximation the probability of every node having at least k neighbors. Efficient algorithms for determining the critical ranges for the purposes of simulation and empirical modelling are developed in =-=[5]-=-, and empirical models describing the convergence of the distributions of the critical ranges to the known asymptotic ones [6] are presented in [7]. As an example of the findings in these studies, one... |

3 | Quantile models for the threshold range for k-connectivity
- Koskinen
- 2004
(Show Context)
Citation Context ... simulation and empirical modelling are developed in [5], and empirical models describing the convergence of the distributions of the critical ranges to the known asymptotic ones [6] are presented in =-=[7]-=-. As an example of the findings in these studies, one may look at Figure 1 which shows the transmission range that, for nodes distributed uniformly at random in a 1 km × 1 km area, provides different ... |